Entropic force of polymers on a cone tip

TL;DR

This paper investigates the entropic force exerted by polymers attached to a cone tip when approaching a surface, deriving universal amplitudes for different polymer models through theoretical calculations and simulations.

Contribution

It introduces a method to compute the entropic force amplitude for various polymer types using epsilon-expansion and simulations.

Findings

Universal amplitude A relates to polymer correlation exponents.

Computed A for phantom and self-avoiding polymers.

Validated theoretical results with numerical simulations.

Abstract

We consider polymers attached to the tip of a cone, and the resulting force due to entropy loss on approaching a plate (or another cone). At separations shorter than the polymer radius of gyration R_g, the only relevant length scale is the tip-plate (or tip-tip) separation h, and the entropic force is given by F=A kT/h. The universal amplitude A can be related to (geometry dependent) correlation exponents of long polymers. We compute A for phantom polymers, and for self-avoiding (including star) polymers by epsilon-expansion, as well as by numerical simulations in 3 dimensions.